[tex] \alpha \: \in \: (\pi, \frac{3\pi}{2} ) = >\alpha\: \in \: cadranul \: III[/tex]
[tex]cos \alpha = - \frac{5}{13} [/tex]
[tex]sin \alpha = ?[/tex]
[tex] {sin}^{2} \alpha + {cos}^{2} \alpha = 1[/tex]
[tex] {sin}^{2} \alpha + {( - \frac{5}{13} )}^{2} = 1[/tex]
[tex] {sin}^{2} \alpha + \frac{25}{169} = 1[/tex]
[tex] {sin}^{2} \alpha = 1 - \frac{25}{169} [/tex]
[tex] {sin}^{2} \alpha = \frac{144}{169} [/tex]
[tex]sin \alpha = \pm \sqrt{ \frac{144}{169} } [/tex]
[tex]sin \alpha = \pm \frac{ \sqrt{144} }{ \sqrt{169} } [/tex]
[tex]sin \alpha = \pm \frac{12}{13} [/tex]
[tex]a \: \in \: (\pi, \frac{3\pi}{2} ) = > sin \alpha < 0 = > sin \alpha = - \frac{12}{13} [/tex]
